Occasionally I get questions from the manufacturing industry about how large of a concentrated load that their existing concrete slab can sustain without cracking. Normally they cannot tell me anything about quality of concrete, size of reinforcement or quality of subsoil. I would like to assume we have a 4" slab, no reinforcement and 2000 psf soil. This seems to be a conservative approach. How do I estimate the capacity. I have looked at the slab as a 4" thick footing with no reinforcement. The concrete would spread out the load at a 45 degree angle and apply the load to the soil. Does this make sense? Am I crazy? I have looked in several books and have not found any documentation on a rule of thumb for concrete slab capacities for concentrated loads. I would appreciate any time you guys could spend on this. Thank you in advance.
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Concentrated load - SLAB on GRADE 1
- Thread starter goboilers
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The capacity of the slab is a function of the Modulus of Sub-Grade Reaction, the tensile strength of the concrete, the slab thickness, possibly fatigue, reinforcing, the loading pattern, the area of load, and the stress of loading on that area for the most part.
The PCA has a program that can reasonably estimate the tensile stress in the concrete based on the above criteria and it's a judgement call from that point on...
There is some argument that 4" is too thin for a significant slab and your dialog with the owner should be clear that he assumes whatever risks are involved (assuming no catastrophic stuff).
The PCA has a program that can reasonably estimate the tensile stress in the concrete based on the above criteria and it's a judgement call from that point on...
There is some argument that 4" is too thin for a significant slab and your dialog with the owner should be clear that he assumes whatever risks are involved (assuming no catastrophic stuff).
As derived from Menétrey in Structural Journal a fc=3 ksi slab on the ground 4 in thick where the load is applied by an 8x8" very stiff plate has limit static punching load of 121 kip plus the load directly supported by the soil through a 30 deg -the flatter- trunk of pyramid, which must be around 4 kip. Hence 125 kip, then apply a safety factor.
Reduce the plate to 4x4” and the limit load is around 65 kip.
Note however that this describes strictly static local punching, for perfectly sound concrete, and this may not be the case for at least any slab on the ground. Other aspects like deflections under the loads etc can have a say, and better recommend the thing be suitably reinforced. More, in any case, punching failure and shear as it is, in the absence of reinforcement the failure is deemed to be fragile. If you had reinforcement enough beyond the working stresses your structure will impart, you'll have further capacity and the failure will be ductile at the end of the moment capacity of the plate, even if the limit punching strength has already been attained. The question is that surely moment capacity of your plate even supported by the ground and reinforced is likely to be the controlling phenomenon.
In the absence of any rebar, I would recommend a bigger safety factor that say, 1.5.
Search in Mathsoft site Collaboratory for Mathcad 2000 , Civil Engineering Folder the sheets
Effect of Wheel Loads on Slabs on Grade
Punching of a RC plate according to Menétrey
Reduce the plate to 4x4” and the limit load is around 65 kip.
Note however that this describes strictly static local punching, for perfectly sound concrete, and this may not be the case for at least any slab on the ground. Other aspects like deflections under the loads etc can have a say, and better recommend the thing be suitably reinforced. More, in any case, punching failure and shear as it is, in the absence of reinforcement the failure is deemed to be fragile. If you had reinforcement enough beyond the working stresses your structure will impart, you'll have further capacity and the failure will be ductile at the end of the moment capacity of the plate, even if the limit punching strength has already been attained. The question is that surely moment capacity of your plate even supported by the ground and reinforced is likely to be the controlling phenomenon.
In the absence of any rebar, I would recommend a bigger safety factor that say, 1.5.
Search in Mathsoft site Collaboratory for Mathcad 2000 , Civil Engineering Folder the sheets
Effect of Wheel Loads on Slabs on Grade
Punching of a RC plate according to Menétrey
I correct myself, if you have steel beyound your plate concrete tensile strength capacity, but not to the extent to be overreinforced, you'll have ductile failure. To have steel of capacity beyond that signified by working stresses in the concrete only means that you have aditional capacity in flexure, but not the characteristics of the failure.
The MathCad Library has a file for designing a concrete slab with a column load on a steel plate. See page 10 of the file list.
One problem is that you often don't know if you have control joints or other cracks at the section in question. Owners always see to be interested in putting slab-supported mezzanine columns on existing column lines which have saw cuts along them.
Use a big base plate and be very conservative!
Use a big base plate and be very conservative!
One limit is the bearing capacity; if you're bearing directly on sound rock, then the upper limit would be the confined concrete compression strength of the slab.
Punching shear gives yet another limit; as noted, 125K or 65K depending on the base plate size.
Another limit is the flexural strength of the concrete; this is determined by the size of the base plate and the soil below. The mathcad solution noted by PEinc yields a load of about 5K based on f'c = 3.5ksi and a 8x10 BPL and a SF of 2 with a modulus of subgade reaction of 200 pci... This would likely be a better approximation of the load capacity of the slab... less with a lesser concrete strength using the square root of the ratios. This could be diminished by existing cracks, reduced thickness, sawcuts, etc. I'm not familiar with the source referenced in the mathcad program, but the thickness required is of a magnitude that I would suspect. The stress can be augmented depending on the placement of the legs; due to the elastic behaviour of the slab, another point load in proximity can increase the concrete stress.
I'll try to run this through the airport slab program from the PCA and see what the concrete stress is...
Punching shear gives yet another limit; as noted, 125K or 65K depending on the base plate size.
Another limit is the flexural strength of the concrete; this is determined by the size of the base plate and the soil below. The mathcad solution noted by PEinc yields a load of about 5K based on f'c = 3.5ksi and a 8x10 BPL and a SF of 2 with a modulus of subgade reaction of 200 pci... This would likely be a better approximation of the load capacity of the slab... less with a lesser concrete strength using the square root of the ratios. This could be diminished by existing cracks, reduced thickness, sawcuts, etc. I'm not familiar with the source referenced in the mathcad program, but the thickness required is of a magnitude that I would suspect. The stress can be augmented depending on the placement of the legs; due to the elastic behaviour of the slab, another point load in proximity can increase the concrete stress.
I'll try to run this through the airport slab program from the PCA and see what the concrete stress is...
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"Designing Floor Slabs On Grade", by Ringo and Anderson is a book that I've always found useful for designing slabs-on-grade. I also suggest that if cracking is unacceptable and the client does not have the slab information, then cores should be taken to establish thickness and compressive strength. A site visit should also be made to look for joints as these will be a consideration.
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